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The problem is the strongly increasing need for computing power with finer resolution. A doubling of the resolution (e.g. from 20 to 10 km) leads to an eightfold increase in computing power.
A twofold increase in the resolution of the computational grid implies that the number of gridpoints increase by a factor of four (two dimensions). Added on top of this is also the temporal resolution as the time step needs to be shorter to avoid numerical instability. Consequently, a doubling of the resolution (or halving of the grid size) implies an eightfold increase in demand for compute power. In addition, also the need for storage of results increases.
Another issue with increasing resolution is that some processes may need to be completely reformulated as they become increasingly resolved. This is the case with convection that is parameterized at coarse resolution but explicitly treated in convection-permitting models. This is a limitation for several regional climate models used in EURO-CORDEX that are not developed for being applied at grid spacing finer than around 10 km.
References
Kendon, EJ, NM Roberts, HJ Fowler, MJ Roberts, SC Chan, and CA Senior (2014) Heavier summer downpours with climate change revealed by weather forecast resolution model, Nature Climate Change, 4, 570–576, doi:10.1038/nclimate2258
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